Andreas Wagner
- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199692590
- eISBN:
- 9780191774829
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692590.003.0206
- Subject:
- Biology, Evolutionary Biology / Genetics
An evolutionary constraint is a bias or limitation in genotypic or phenotypic variation that a biological system produces. Striking phenotypic examples include the absence of photosynthesis in higher ...
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An evolutionary constraint is a bias or limitation in genotypic or phenotypic variation that a biological system produces. Striking phenotypic examples include the absence of photosynthesis in higher animals, and the general lack of teeth in the lower jaw of frogs. Constraints can influence the spectrum of evolutionary adaptations and innovations that are accessible to living things. Based on the cause of constrained phenotypic variation, one can distinguish physicochemical, selective, genetic, and developmental constraints. The latter class of constraints emerges from the processes that produce phenotypes from genotypes. This chapter examines these four causes for molecules, regulatory circuits, and metabolic networks in the genotype space framework. This framework shows that processes of phenotype formation cause the three other classes of constraints. It can help us appreciate why causes of constrained variation are often entangled and not clearly separable. The chapter also shows that the kind of evolutionary stasis that occurs during punctuated and episodic evolution is a consequence of genetic constraints, whose origins the genotype space framework can readily explain.Less
An evolutionary constraint is a bias or limitation in genotypic or phenotypic variation that a biological system produces. Striking phenotypic examples include the absence of photosynthesis in higher animals, and the general lack of teeth in the lower jaw of frogs. Constraints can influence the spectrum of evolutionary adaptations and innovations that are accessible to living things. Based on the cause of constrained phenotypic variation, one can distinguish physicochemical, selective, genetic, and developmental constraints. The latter class of constraints emerges from the processes that produce phenotypes from genotypes. This chapter examines these four causes for molecules, regulatory circuits, and metabolic networks in the genotype space framework. This framework shows that processes of phenotype formation cause the three other classes of constraints. It can help us appreciate why causes of constrained variation are often entangled and not clearly separable. The chapter also shows that the kind of evolutionary stasis that occurs during punctuated and episodic evolution is a consequence of genetic constraints, whose origins the genotype space framework can readily explain.
Peter Mann
- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations ...
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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.Less
This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
